Methods of the kind mentioned alone as well as a suitable circuit arrangement for carrying out the method are basically known from Published German patent application No. 30 36 830, the teachings of which are based on the teachings of German patent specification No. 16 38 032 and of Published German application No. 27 29 657. The use of interpolating means, consisting of an interpolating computer for a computation of intermediate values is known from U.S. Pat. No. 3,618,073.
In theory, aan interpolating computer can be used for a computation by which each of the signal periods, which may represent increments of a scale, can be subdivided as desired so that the desired resolution in the display or processing can be achieved independently of the magnitude of the increments of the scale. It is quite conventional in practice to subdivide the periodic signals obtained by a scanning of an incremental scale by a factor of 100. For this purpose, interpolation tables are prepared and stored and the interpolation table is read at addresses associated with instantaneous magnitudes of the measured-value signal or of a signal obtained by a transformation or correction of the measured-value signal. The stored value is then used as an interpolated value for the further computation or for the display or processing. In most cases, complete signal periods are accumulated by counting means and, where purely incremental scales are used, the direction of the scanning movement is also determined from the analog signals. In absolute systems having a very fine incremental trace, the absolute values are combined in a succeeding device with the interpolated values which have been computed.
In the display or processing, e.g., in control systems for machines, a high resolution will not make sense if the possible accuracy of the display differs excessively in order of magnitude from the accuracy of the measurement which can actually be achieved.
The accuracy of the measurement which can actually be achieved depends, inter alia, on the precision of the scale, on the exact agreement of the direction of the scale and the direction of the scanning movement, on the accuracy of the scanning operation, on the maintenance of the proper phase displacement between the generated signals, on the maintenance of a predetermined waveform and amplitude of the signals and also on external factors, such as defects of the machine tools on which devices on the present kind are used to measure lengths or angles.
In order to compensate such possible errors and to achieve a measurement which is as accurate as possible, the earlier methods of measurement of the type mentioned described above are carried out in such a manner that the signals delivered by the interpolating device are corrected. For this purpose, these signals are combined in the correction data computer with previously stored correcting values. Whereas this method has proved to be useful, it involves a very high cost because in the usual practice a correcting value is stored for each interpolated value which can possibly be obtained throughout the range of measurement. It will be understood that the absolute values of said correcting values may differ from each other and that said absolute values must be stored as corresponding stored values. For this reason, different stored values must be stored at each memory address. Hence the method requires very large and highly expensive memories. Because very large correcting values would be obtained in certain regions of the range of measurement in case of systematic scale errors, i.e., if the actual number of increments along the range of measurement differs from the specified number, it is also known to determine the systematic scale error for each section of the range of measurement and to store for each section of the scale a correcting value determined in dependence on the mean function of the systematic scale error and which is also taken into account in the computation of the values for correcting the measured values. In order to reduce the storage capacity required for scale sections in which similar error functions can be expected, an average error function for each signal period can be assumed for such section and can be taken into account by the storage of a corresponding correcting value in the correction data memory. While this practice will reduce the required memory capacity, the accuracy of the correction will be strongly affected thereby. Specifically, this approach hardly permits of a compensation of errors in measurement which are due to machine defects.